A method of constructing adaptive hexahedral moving grids

A variational method of constructing an adaptive moving grid composed of hexahedral cells is considered. The method is based on minimizing a functional defined on the Riemannian manifold in space of variables including the physical space coordinates and components of a vector-valued monitor function. The mesh is generated in the manifold and then it is projected down to the physical region to provide the adaptive grid. The integrand of the functional is the non-dimensional ratio of the invariants of the metric. The functional depends on metric elements of two metrics. The curvilinear mesh, generated in the manifold, induces the monitor metric. Another control metric, defined in a special way, is responsible for additional cell shape control. The issues of non-degeneracy conditions for a hexahedral mesh are considered. Examples of adaptive grids are presented.